One polite follow-up is reasonable if the referrer has not responded and you have a real application deadline or action pending.

Give them enough time to act, especially around weekends or busy project periods, and keep the message short.

For example, remind them of the upcoming submission date and ask whether they need anything else from you.

If there is still no response, submit through the normal process rather than sending repeated reminders.

imo I would not make the referral the goal of the first call.